DOCUMENT RESUME

ED 025 752 AL 001 636

By-Reich, Peter A.The English Auxiliaries: A Relational Network Description.Yale Univ., New Haven, Conn. Linguistk Automation Project.Pvb Dare Nov 68Note-44p.EDRS Price MF -$0.25 HC-$2.30Descriptors-English, Negative Fo.-ms (Language), *Structural Analysis, *Syntax, VerbsIdentifiers-*Relational Network App. oach, Stratificational Grammar

In this paper the author attempts to show that the relational network approachis adequate to handle the relationship between interrogative and declarative wordorder, the gramatically determined "do," "not," and the order of morphemes in theverbal auxiliary. He feels that this is one step toward demonstrating that therelational network approach is a viable alternative way of formalizing our knowledgeof English grammar. (See relate" document AL 001 634.) (Author/DO)

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THE ENGLISH AUXILIARIES:

A RELATIONAL NETWORK DESCRIPLION

Peter A. Reich

November 1968

"PERMISSION TO REPRODUCE THISMATERIAL HAS BEEN GRANTED

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Linguistic Automation Project

YALE UNIVERSITY

New Haven, Connecticut

AL 001 636

THE ENGLISH AUXILIARIES: A RELATIONAL NETWORK DESCRIPTION

Peter A. Reich

The paper, "Symbols, Relations, and Structural Complexity" (Reich,

1968b), discusses an alternate formalsm for context-free phrase struc-

ture grammar (Chomsky and Schutzenburger, 1963). This formalism consists

of networks of relationships, a slightly refined version of the networks

proposed by Lamb (1966a; 1966b). Three types of relations are needed

to achieve a formalism equivalent in powea- to context-free phrase struc-

ture grammars: downward concatenation (downward ordered and), downward

disjunction (downward unordered or), and upward disjunction (upward

unordered or). Two additional nodes are introduced which do not add

to the power of the system, but do contribute to simplicity of the struc-

ture and its flormal properties; namely, downward ordered and-or, and

downward optional. These networks of relationships have certain Bprmal

properties; among them are associativity, bypass representation,

commutivity, distributivity, coincidence, and reduction. The formal

properties define equivalence relationships among different networks.

Figure 1 summarizes these relationships.

All of the discussion in that paper is limited to grammatical

structure essentially equivalent to context-free phrase structure gram-

mar. Chomsky and his followers have argued, and we heartily agree, that

this is not enough. Chomsky (1957:68) writes:

SYM

BO

L

_

NA

ME

--1

A

ASS

OC

IAT

IVIT

Y

B

BY

PASS

RE

PRE

SE1,

. AT

ION

C

CO

MM

UT

IV r

r Y

D

DIS

TR

IBU

TIV

ITY

E

CO

LIC

IDE

NC

E

R

RE

DU

CT

ION

A

downward

concatenation

(downward

ordered and)

No

downward

ordered

NO

/_I

._

:17

A

downward

disjunction

(downward

unordered or)

:-

AE

AbA

la

cca t)

'

*

upward

disjunction

unordered

or)

-

15.

1)

E

ownvard

od

onaptil

- A

-1

i

=_ _

Figure 1:

Summary offormal Properties

I%)

3

We have seen that a wide variety of apparently distinct

phenomena all fall into place in a very simple and natural

way when we adopt the viewpoint of transformation analysis

and that, consequently, the grammar of English becomes

much more simple and orderly. This is the basic requirement

that any conception of linguistic structure (i.e., any model

for the form of grammars) must meet. I think that these con-

siderations give ample justification for our earlier conten-

tion that the conceptions of phrase structure are fundamentally

inadequate and that the theory of linguistic structure must be

elaborated along the lines suggested in this discussion of

transformational "analysis.

Many have concluded from this and other such statements that the

only grammars which are adequate are grammars that contain transforma-

tions. While we agree that phrase structure is fundamentally inade-

quate, we do not therefore agree that the theory of linguistic struc-

ture must be elaborated in terms of transformations. There can be no

doubt that a theory consisting of phrase structure plus transformations

is considerably superior to phrase structure alone. But, we find, 'As

the depth of the analysis increases, problems mount to the point

where they indicate a serious inadequacy in a grammar that consists

only of rewriting rules. Nor is this particular difficulty overcome,

as many others are, when we add transformational rules to the grammar.'

(Chomsky, 1965:80). It is certainly possible that phrase structure

plus transformations plus distinctive features plus projection rules

plus...will bring us closer and closer to an adequate theory. But it is

also possible that another theory could do the job easier, faster, and

S.

with considerably less theoretical structure. It is with this aim in

mind that the relational network approach is being developed.

In order for one model to be shown superior to another model, it

is necessary to show that it handles all of the data least as well as

the other theory, and some of the data considerably better, or else some

data not covered at all by the other theory. In linguistics this is an

unending task, especially since the difFerent models are continually

being modiFied. Thus in the attempt to promote our mode] here, we can

only make a small dent in the subject matter that needs to be discussed.

We choose to discuss the English 'auxiliary verbs', because Chomsky

believes that 'The study oF these auxiliary verbs turns out to be quite

crucial in the development of English grammar' (Chomsky, 1957:38). We

hope to show that we cFn obtain the same kinds of insights as can the

transformationallst.

The problem of the English auxiliaries is that such constructions

as has been taking are most efficiently described as consisting of dis-

continuous constituents. A phrase structure grammar would produce

(s) (have en) (be ing) (take), and a transformation rule would reorder

the oonstituents -- have s be en take ing. (Chomsky, 1957:38-40; Klima,

1964: 253)

In order to handle this construction, we must include some Features

in our model beyond those given in figure 1. We want to do so without

adversely affecting some of the nice features we have developed, such

as the simple complexity count and the formal operations which give us

equivalence sets. What we need is simply some new nodes. In particular,

we need upward cEljunction, diagrammed as shown in the top row oF

symbol

name

A

associativity

bypass

oommutivity

1

representation

UCJ

upward

conjunction

(upward

unordered

and)

a

distributivity

ooincidence

distribution

over

concatenation

reduction

1

UOP

upward

optional

downward

precedence

disjunction

(downward

ordered or)

EVD

free

_1-

variation

disjunction

Figure 2:

Some additional nodes needed

6

figure 2.1 What this node means is that two conditions, b and c, both

must be satisfied before a is produced. For example, both zo.and past

must be present in order to get went, and both bad and comparative must

be present in order to get worse. In terms of signals, signals must come

down both b and c, not necessarily timultaneously. A signal is sent down

a immediately after b or c comes down, whichever comes later. Feedback

which goes up a travels up b and c simultaneously. In terms of formal

properties, they are similar to concatentation, except that the relation

is oammutative. There is an additional property, distribution over oian-

catenation (see figure 2). This says that if condition d is required

before a can be realized as b followed by c, the requirement (i.e., the

upward conjunction) can be placed on the a, b, or c lines of the concat-

enation element. For the same reasons that we introduced the downward

optional element and the downward ordered and-or in Reich, 1568b, we

introduce the upward optional2and the upward unordered and-or.

(4)

re

r, 4 rer- , ,

(7-) (-31

A(Dc.7) *Dcr)t(wr)

(tAtZ)

Figure 3: Simplification leading to identification

of discontinous constituent.

7

Figure 3 shows the role of upward conjunction in the simplification

process. It is highly suggestive as a model of the process by which a

child learning his language learns to discriminate its parts, even IF

they are noncontiguous. Network (1) would represent the condition in

whiz:h the child learned that the concept of eatina conjoined with the

concept of perFect tense is expressed by haevetn, while the concept

of eating together with the concept of present tense is expressed by

We see that by applying the formal properties, we can move step by step

to the simplegtequivalent network (6). This network expresses the gen-

eralization that perfect tense is realized as the discontinuous consti-

tuent hmv n, and the concept of eating is realized in both the per-

fect and present tenses as fft. We see that the initial information we

represent in our networks is not just the form, or expression, but

also the meaning, or content. This represents a major difference betmen

our approach and that of many transformationalists. The production of

discourse consists not in moving from abstract to concrete, but rather

in a transduction process between content and expression (Gleason, 1564;

Lamb, 1966c: 562ff). In this we follow Hjelmslev (1943:47-60) and agree

with Chafe (1567: 84-89).

In order to understand the English auxiliaries, therefore, we not

only need to know the patterns of English expression, but we must have

a model of the patterns of English content. The model we shall use is

that of Halliday (1967). According to this model, there are three basic

tenses in English: past, present and future.3 Complex tenses can be

built up by ooncatenation of the simple ones. For example, future past

(as in I will have finished it ...) means that whatever event we are

talking about will in the future have taken place in the past. Halliday

8

calla this past in future. In this framework the form of the verb in

such examples as I am Helping, which as been called progressive

(e.g., Palmer, 1965:59), temporary aspect (e.g., Jocs, 1964:106), and

various other things, is present present, or present in present.

Similarly, the form or the verb in such example9 as I have died is

represented in this framework as present past, or past in present, and

I had died is represented as past past, or past in past. Halliday has

recorded examples of the concatenation of up to five tenses. For

example, He had been going to have been takin ... would be an example

of pastp_a_s;tf.tittn_-easta-eseri According to this framework, each

basic tense has two realizations. Present is realized as either

nothing (91 or be-ing. Past is realized as either ed or have-en.

Future is realized as either will or 122.119ingata. Of course, most of

these in turn have alternate realizations -- e.g., be is realized in

portmanteaus as am, is,are, etc. We shall refer to the first of the two

alternate of realizations of basic tense as type I, end the second as

type II. Type I realizations occur in simple tenses and as the first

tense in all finite constructions. Type II realizations occur in non-

finite oonstructions and in complex tenses.

We shall first consider the nonfinite constructions. These are

the only constructioas that are permitted when verbal constructions

are nominalized, as in:

To publish the journal on time-)was difficult.

Publishing the journal on time ,

The nonfinite does not include the full verb phrase. One cannot say:

*To can avoid the draft is his goal.

*Wenting to Vietnam cost him his life.

9

Halliday finds twelve tenses available to nonfinite constructions, as

shown in figure 4 (d = past, f = future, p = present, s = passive).

To each of these twelve tenses can be added a passive, which gives us

fd

dp

fp

df

dfd

fdp

dfp

dfdp

to take

to have taken

to be taking

to be going to take

to be going to have taken

to have horn taki;)g

to be going to be taking

to have been going to take

to have been going to have taken

to be going to have been taking

to have been going to be taking

to have been going to have been taking

Figure 4: The twelve nonfinite tenses

such constructions as (s) to be taken, (fds) to be going to have been

taken, (dfs) to have been going to be taken, and (dfdps) to have been

going to have been being taken. It will be granted that some of these

constructions require fairly uncommon contexts in order to be produced,

but Halliday has examples of many of these from natural conversation

recorded on tape, so we shall take his word about the data. If we dia-

gram all these and simplify, we get figure 5, which was first proposed

by Newell (1966:82).

10

Figure 5: Phrase structure component of

nonfinite construction

The finite consists of a modal auxiliary, or past, present or

futgo, concatenated with the nonfinite system. If we include this in

our diagram, we get figure 6. But the tenses in the nonfinite part

are type II, while the initial tense is type I. The fact that they have

Figure 6: Phrase structure component including

finite construction

the same meaning indicates they are brought together by a disjunction

above this point.4

We now have two independent factors controlling our

grammatical decisions whether the tense is past, present, or ftrure,

11

and whether we are in the nonfinite portion of the predicate construc-

tion or not. Thus we need upward conjunction to indicate that both fac-

tors must be combined. This is diagrammed in figure 7. We have also

included the top portion of the structure which realizes the type II

tenses. In the diagram we analyze the type II future, be going to as

(be ing) sp to, where be ino is the same construction as the type II

present. The be is the same as the be of the passive be en, and the

en of the passive is the same as the en of have en. What I mean by

this is that no matter whether the be came from be en or from be ing,

it will be realized a particular way, depending upon person, type I

tense, and number (e.g. am, is, are, etc.), but not depending on

what construction it came from. Similarly, en has many alternate

t L."

t41

es'eCt

fl

?1.(I

0 e0- 4(/ .

t.P,49"t°

Figure 7: Grammar with Type I - Type II

tense disjunction added

ell

.4NIMMNIm

12

realizations, depending on what verb it is to be associated with, but

not depending upon whether it came from be en or have en.

Let us now consider what happens when negation is present. nt is

affixed to be, have, will, or any of the modals, whichever comes first.

If none are present, a do is inserted. Thus they have gone combined

with negation yields they haven't gone, but they went yields they didn't

Esl. Figure 8 shows the grammar for figure 7 with this additional infor-

mation added. The structure we have added corresponds closely to the

way we described the facts in English. We have added concatenations

saying that after have, be, or the modals including will we insert nt

if we have a negation signal from content. In the case of 3impJe past

or present, none of these occur. In this event nt is realized following do.5

We have at this point used a type of element which we have not

previously discussed -- the downward precedence disjunction (downward

ordered or). In order to understand this we shall have to look at the

meaning of disjunction in our system more closely. When we were

dealing with context-free phrase structure grammars, we defined disjunc-

tion by saying that a signal oaming in a would go down either b or c;

the choice was a random one (Reich, 1968b: figure 8). Thus we would

generate one of the set of possible sentences at random. But of course

we don't generate sentences at random. In reality we generate (barring

errors) just that sentence which we want to generate. Our system is

selectively generative; it is generative under content control. This

notion is probably one oE the most important contributions Lamb has

made. In terms of our network structures this means that each

nonft'n'itt

iity_{ 10n

Figure 8: Grammar with nezation added

disjunction leads down to one or more upward conjunctions which determine

which one of the possibilities is realized. Thus in 9(1) for a given

segement s may signal or t may signal, but it will never happen that

both s and t signal. (The zir-gag line means there may be additional

nodes between the nodes referred to.)

114.

precedencere5tAgar.crec vetriat,'ori

Figure 9: Types of disjunction

cordct,91

This is the condition that we place on regular disjunction, but we

do not want to limit ourselves to this situation. Figure 9(2) describes

another situation. Here s or t may signal, but it is also possible that

both s and t may signal. In this situation we must define what we want

the grammar to produce. We may decide that when both signal, s is to

be realized, and t is to fail. Thus s takes precedence over t. We shall

call this precedence disjunction. An example of this is used in figure

8 at point X in the diagram. If passive (s) and negation both occur,

the passive construction is realized, and do is not needed.

In some situations we don't know what the variables are that

determine why an informant makes one choice over another. They appear

to us to be random. This is the ease of free variation. We can indi-

cate this with another disjunction node, this one to make its decision

15

at random. We shall call it the free variation disjunction, shown in

9(3). As our object is to specify as completely as possible the con-

ditions which determine precisely the expression that a particular con-

tent produces, one of our goals is to have as few free variation disjunc-

tions in our grammar as possible. However, in any practical study of

grammar, we shall have to have these around. The formal properties of

precedence and free variation disjunctions are given in figure 2.

Still another disjunction situation arises. We shall term this

the conditional disjunction, after the conditional statements in LISP

and Algol-like computer programming languages. This is the situation

in which of the two possibilities, one has a condition on it (leads to

an upward conjunction), and the other does not, as shown in 9(4).

If the condition s is satisfied, the former possibility is taken,

otherwise the latter path is chosen. This is very similar to the

precedence disjunction, although logically distinct from it. In this

paper the two situations will not be distinguished. It is possible

that certain behavioral models of behavior may require that the two

situations be kept distinct.

A similar differentiation of oancatentation into four separate

cases is also useful in defining the performance characteristics of

the relational elements. The differentiation into four cases is

based on the conditions-under which the concatenation element can fail.

The four logically distinct possibilities are pictured in figure 10.

The first possibility, 10(1)lis simply that if a signal oames in a, the

concatenation will never fail to be realized. This possibility is

common in the tactic and sign patterns of linguistic structure.

16

iricalbbk

(2)

b-ca 110114.

(3)

c--fes 11;61e,

rigure 10: Types of concatenation

b-oY- c - 10,.le.

All concatenation elements in figure 8 except the two discussed below

are of type (1). In the case of the concatenation above the modals,

labelled M in figure 81 we have an example of a type (2) concatenation.

The b wire may succeed or fail, depending upon whether or not the

higher stratum signals the presence of a modal or will, but the c wire

will always succeed.

A third possibility, 10(3)lis that the concatenation may fail as

a result of a condition on the c wire, but the b wire will always

succeed if a signal is sent down it. These are considerably rarer,

but occasionally occur in tactic patterns. An example appears in

figure 8. In the case of the concatenation element above the do

(starred in figure 8), it is the success or failure of the c wire

which determines whether the concatenation will succeed. That is,

it is the presence of negation (and other things which we will add

below) that determines the presence of do in the utterance. This,

17

then, is a type (3) concatenation element.

A fourth possibility would be that both conditions on the b wire

and conditions on the c wire could independently cause the failure of

the concatenation element. This is pictured in 10(4). I have not yet

come across this possibility in grammars attempting to describe frag-

ments of natural language.

Ideally, all four possibilities should be realized by a single

type of node. However, in the current encoding model (see appendix to

Reich, 1968a) we have not been able to accomplish this. Two different

concatenation elements have been defined, type (2) and type (3). Type (1)

can be considered as a subcase of either (2) or (3). We have arbi-

trarily considered it a case of type (2). In the figures of this

paper, type (3) concatenation is starred, otherwise we shall not be

concerned with the difference between these two types of concatenation.

One of the 'apparently distinct phenomena that Chomsky finds

falls into place is the yes-no question. What appears in the declar-

ative Bonn as Meredith has dropped acid becomes in the interrogative

Has Meredith dropped acid? When no auxiliary is present, do is added,

as it is in the case of negation. Thus the declarative Julia Child

eats TV dinners becomes Does Julia Child eat TV dinners? Chomsky

says (1957:64):

The crucial fact about the question transformation T

is that almost nothing must be added to the grammar in order

to describe it. Since both the subdivision of the sentence

that it imposes and the rule for appearance of do were required

independently for negation, we need only describe the inversion

18

effected by T in extending the grammar to account for

yes-or-no questions. Putting it differently, transforma-

tional analysis brings out the fact that negatives and

interrogatives have fundamentally the same 'structure,'and

it can make use of this fact to simplify the description of

English syntax.

We shall see that relational network analysis also brinl's out

these facts. Figure 11 contains the additional structure necessary

to account for yes-or-no questions. Let us see what we have added.

First we have added the information that a declarative consists oF

the subject followed by the finite. The only atructure necessary to

include the interrogative construction is the addition of interrocr,

a line coming from content which attaches to the finite construction,

and the addition of an and-or at Y which attaches to the subject line

at Z. The result of the former connection is that in the case oF a

yes-no interrogative the sentence begins immediately with the finite

construction. The result of the latter connection is that the subject,

if it hasn't already occurred, occurs in the same place as the nt,

and has the same effect of adding the do when other auxiliaries are

not present as does the negation. If the negation also occurs, the

order is nt followed by the subject. Thus we have added the inter-

rogative with very little additional mechanism, just as Chomsky does.

We have made two additional small changes to the grammar oF

figure 8. In figure 11 we have added the copulative, be, in the same

place as the passive (indicated by s). This has the effect of adding

Mr,

19

Figure 11: Grammar with interrogative added

the copulative be to the list of words which don't get do in interroga-

tive and negative, accounting for the fact that Chomsky is another Freud

in the negative is Chomsky isn't another Freud rather than *Chomsky

doesn't be another Freud, and similarly in the interrogative. The same

20

is not true when have is the main verb: at least in American English.

Thus Americans would say Don't you have an electric toothbrush? rather

than *Haven't you an electric toothbrush? This means that the main

verb have2

combines with the auxiliary have below point X. Both haves

become had in the past and has in the 3rd person singular present, SD

we know they come together above the structure which handles this. In

those dialects in which Haven't you an electric toothbrush? is acceptable,

the line from the main verb have would come in above X but below the

concatenation with en, as shoum in the insert of figure 11.

So far, we have developed our grammar to the point where it can

produce a good portion of what we can find in the auxiliary system.

Houmver, the segments are coming out in the wrong order. Lma_Eirla

to have been finished with my income tax by now, but.., would come out

of our grammar I d1 be ing go to have en be en finish with Chomsky

finds that transformational rules make the necessary reordering very

simple. Affix followed by verb is to be rewritten as verb followed by

affix, where verb includes modals, have, be, etc., and affix includes

past, en, ing etc. After this rule is appled there is a large number

of rules of the form: do past-odid, do en-Adan, do neg-Adönt, do sing -

ular.4daz, etc. (Chomsky, 1957: 39-40)6 We could, if we wanted to,

represent these rules in our network. However, there is a simpler way.

First of all, all of the modals and have7

, be, and do are irregular,

that is, they have alternate phonological realization depending upon

morphemic context. Why take two steps to go from past do to do past

to did when it is just as easy to state the rule past_st-Adid? In our

system this course seems simpler. And what about the generalization

21

that no matter what the morphemic context of do, the initial phoneme is

always d? The structure I propose allows one to make such generalizations.

Although such generalizatiuns are relatively trivial and uninteresting,

the formalism developed to describe linguistic structure should be

flexible enough to allow such statements. We shall see how they can

be made within the relational network framework.

Let us first look at the structure which will account for regular

verbs, shown in figure 12. We see that following the regular verb there

Figure 12: Structure for regular verbs

is the possibility of three different endings. In the environment of

past I or en, the ending is d. In the environment of present I there

are two possibilities: if additionally the environment includes aa

22

person and linp_l_AE, the ending is z; otherwise there is no ending

(or ing - we shall see how this is produced later). In the event that

neither os_t_I or en nor present I occur, the verb is realized without

an ending.

Although the diagram is a straightforward representation of the

facts, it does not fit into the patterns proposed by Lamb (1966b).

Specifically, it appears to put into one stratum information that Lamb

preferred to split into two strata, lexemic and morphemic. It is my

feeling that if the requirements for what is allowed in the realizational

portion of linguistic structure are relaxed slightly, the information

Bormerly described in these two strata can be combined into one stratum.

This is a rather involved empirical and theoretical question, the

discussion of which I shall save for a future paoer. For the purposes

of this paper the reader should simply be warned not to expect the

diagrams in this paper to conform completely with all of Lamb's 1566

hypotheses.8

Let us now tUrn to the structure of some irregular verbs, to see

how filey can be handled. Figure 13 shows the structure I propose for

do. The initial consonant is d no matter what the environment is.

There are two sets of environments to be considered. The first choice

is based on whether do occurs with present I, past I, or en. If it

is past I the vowel is i and the final consonant is d. If it is en

the vowel is a and the final consonant is n. Note that the concatena-

tion is type 3; the choice of vowel is determined by what follows. If

do occurs together with present I, then a second set of contexts deter-

mines the vowel. In the environment 3rd -person singular the vowel is a

23

and the final consonant is Z. If not (precedence disjunction), but if

the context includes Ligl (negation), the vowel is 5. Otherwise,

(conditional disjunction) the vowel is M.

Im111/0

Figure 13: Structure for do.

The structure of go and will, show in figure 14, is similar to

the structure of do. In the case of go the same three contexts deter-

mine which form is realized, but this time one form, wenD, which is

realized in the environment past I is entirely distinct from the other

two forms, which begin with R. The fact that the other two forms

differ in their vowel can be described either morphophonemically, that

is, as being determined by the environments en or present I as the case

24

Figure 14: Structure for za and will

may be, or phonemically by the presence of a following n or some such

rule. The representation shown in figure 14 is the morphophonemic one.

The D in wenD is a special morphon which devoices a following d, so

MN/Dd/ is realized as P/t/. Otherwise MNthat /D/ is realized as d.

Thus MN/benDd/ is realized as P/bent/. Similarly with send, sent, and

lend, lent. Will is realized as wd in the environment neg, otherwise

as wil.

Figure 15 gives a possible description of one of the most compli-

cated morphological structures,namely that of be. Here again we find

two levdls of choices. The first is unique in that there are four

choices. In all other verbs the infinitive andim form of the verb

is the same as that of present 1, SO that these lines come together (at

25

Figure 15: Structure for be

the upward disjunction marked X in the figure) and act as a single

conditioning environment, labelled present I in figures 12, 13, and 14.

In the verb be the forms are distinct, as dhown in figure 15. In the

second level of choices we find the familiar 3rdasim, but in addition

we also find nelzaTest (which will be discussed in detail below) and

1st-sing as conditioning environments. I will leave it to the reader

to check.out that the diagram does indded produce am, is, are, was,

were, be, being, and been when appropriate.

Thus far I have described the realizational structure of various

26

verbs as if they were separate and completely ideosyncratic. This is,

however, not the case. Go and do(and all the irregular non-modal verbs)

behave like regular verbs with respect to 3rd-sing in having the

ending z. Other facts can be generalized over fewer verbs, such as en

being realized as n in been, done, gone, taken, etc. Still other facts

apply to as few as two verbs, such as the 6 for the vowel of the verb

in the presence of neg which is only true for won't and don't. This is

no particular problem for a network grammar. The descriptions given in

figures 12 through 15 are easily combined and simplified to represent

identical structures only once, and to identify specifically the class

of items for which the structure applies. The resulting structure is

shown in figure 16. For example, the upward disjunction at X in the

center of the figure defines the class of verbs that take n as the real-

ization of en.

Again I wish to emphasize that this diagram is not necessarily

the optimal way of representing this grammatical information within a

relational framework. That is beside the point. Representing these

facts as a network seems superior to transformational grammar alterna-

tives. If one represents these facts in a lexicon; that is, a list oF

separate lexical items, one is not able to state the partial generali-

zations that occur. One is condemned to inefficiently repeat the rules

over and over again in each item for which they apply. If one writes

transformational rules to describe the partially generalizable struc-

tures, one is faced with the problem of how to specify when a transfor-

mation Is applicable. There is another problem one encounters with

this approach. Notice that while the realization of, for example, do

vey1". 1,04

0'10

ree-(see 1r`c

Figure 16: A fragment of realizational structure

is determined by the environment of en, it is also true that the reali-

zation of en is determined by do. In a rewrite rule framework, one could

28

express these facts with rules of the form:

(<3) a-tx / b and (118) b-->y / a

The problem is that these rules in a rewrite framework must be

ordered. We want ab to be realized as Isz. But if we order the rules

,(2iN'ab would be realized xb, and if we order the rules fr( ab would

be realized 22,.. One can always get around this problem in a rewrite

framework by means of a special rule of the form ab4xy, but this has

the disadvantage that within the grammar a is not related to x and b is

not related toz. But do and da are certainly related and en and n are

certainly related. Obe might propose a rule doida/ n, except that

this would result in don't being realized as dant. This can be avoided

by inserting an initial rule do->d6/ neg, so that our rules are ordered:

doodoj neg

en.in/do

do.ida/ n

neont

This has the disadvantage of separating the two rules for do. It also

forces an ordering between a rule concerning !lea and a rule concerning

en, which seems ad hoc since they never occur in the same word. It

seems to me that the best solution is to allow simultaneous application

of rules, if one must use rules at all.9

We now turn to the problem of order disparity in relational networks.

If we put together the networks of figures 11 and 16, we notice that

the original ordering of elements is not the one that is ultimately

realized. Figure 17 shows an example. We notice that the grammar above

the dashed line produces have en be ing. But the network below the

29

dashed line specifies that the order should be bi n rather than en be.

If we are not interested in a perfprmance model we can simply state

the general principle that lower level orderings take priority over

higher level orderings.

n4..

'have

Figure 17: Example of order disparity in

relational networks

How can such a principle be realized in a performance model? In

earlier papers (Reich, 1968a:2-7; Reich, 1968b: 11-14) it was explained

that concatenation ordering works by means of a feedback signal. Thus

a signal does not start down B in figure 17 until a feedback signal

30

oames up A, in effect signalling that the entire structure emanating

down from A has been successfully realized. But en can't be realized

until after a signal is sent down B. The conflict is easily resolved

by adding a node of a new type, a 'feedback reflector' at X. When

a signal comes down to a feedback reflector, it continues to send the

signal down the wire, but it also sends feedback up the wire immediately.

When feedback finally does oame up to the feedbadk reflector, it simply

stops, since feedback has already been sent up from there.

In the grammar of English auxiliaries discussed in this paper,

the feedback reflector must be added at four places, present-I,

past=1, en, and ing. This simple addition to the theory allows one to

handle both anataxis and discontinous constituents.

The last area we shall discuss is the problem of negation. The

problem arises because of the missing amn't in English. In my normal

speaking dialect I say I'm not when the subject appears before rhe

auxiliary, and aren't I in interrogatives where the pattern is -irst

auxiliary before subject. The question is wny aren't I rather than am

I not. This question leads to the problem of meaning in negation. Of

the three accounts of negation I looked at (Klimi, 1564; Palmer, 1565;

and Joos, 1964) two offered suggestions as to the meaning of not.

Palmer (1565:43) suggests that of the two forms of not, n't modifies

the modal auxiliary and not modifies the non-finite form that follows

it, and that n't should be oonsidered to precede the auxiliary to

which it is affixed. Both of these suggestions seem overly simplified.

Consider the sentences in figure 18 (the apostrophe indicates emphasis,

probably realized by intonation). We see that what is emphasized is

31

18a. Zellig didn't stay at the 'hotel.

Zellig didn't 'stay at the hotel.

18c.'Zellig didn't stay at the hotel.

18d. Zellig didn't stay 'at the hotel.

18e. Zellig 'didn't stay at the hotel.

18f. Zellig did 'not stay at the hotel.

18g. Zellig 'did not stay at the hotel.

18h. 'Didn't Zellig stay at the hotel?

18i. Did Zellig 'not stay at the hotel?

Figure 18

(He stayed at the 'inn.)

(He moved into a 'flat.)

(but 'Rulon did.)

(He stayd 'in it.)

(He commuted daily from home.)

(contrary to What you thought.)

(as you had suspected.)

(No, he didn't.)

(Yes, he did not.)

=1111S

what is negated. In 18a hotel is negated, but the rest of the sentence is

not. In 18b stay is negated. In 18c Zellig is negated. In 18d at is

negated. In 18e the entire predicate seems to be negated, and in 18f only

the polarity ,)f the sentence seems to be negated. But 18e and 18f can

both mean either; the difference seems inbe only a tendency. Thus in the

fifth previous sentence in this paragraph, I prefer is not to isn'tlbut

would accept either. In 18g not modifies stay at the hotel, but the

predicate is considered a positive act. This is best seen in 181, which

is the interrogative of 18e. In general, the parenthesized phrases or

clauses to the right of each of the examples cannot be concatenated with

examples other than the one they are with. Thus, for example, 'Zellig

didn't stay at the hotel; he moved into a 'flat. is less acceptable, if

not ungrammatical.10

Neither Palmer's nor Joos' suggestions can account for the variety

shown in examples I8a through 18g. Nor do they account for the diff-

erence between 18h and 181, since do in these sentences has no meaning.

32

Moreover, we find that not cannot occur anywhere in the verb phrase;

it can occur immediately after the first auxiliary in the form n't or

not, and it can occur immediately before the main verb.11 Thus 1,

19t, and 19d are grammatical, but 19c is not. Based on these examples

1St. She wasn't going to have typed the thesis.

19io. She was not going to have typed the thesis.

19c. *She was going to not have typed the thesis,

19d. She was going to have not typed the thesis.

Figure 19

we conclude that there are two types of negation: indefinite negation,

which is realized immediately after the first auxiliary, and which has

as its range that part of the sentence which is emphasized, and definite

negation, which indicates a positive act not to do something, and

which occurs immediately before the main verb. These two negations are

independent of one another; they can both occur in the same sentence:

Zellig didn't not stay at the hotel. When there is only one auxiliary

the two slots occur at the same place in the sentence, resulting in

ambiguity in the written, but not in the oral, forms, as in 18f versus 18g.

Given this description of not, we can understand why in the indi-

cative I say I'm not, while in the interrogative I say aren't I. The

missing amn't, corresponding to 18e is not a problem because of the

existence of the alternate form I'm not, corresponding to 18f. But

am I not doesn't work, because this is definite negation, and means

something different. Thus a contracted form must be used, and the one

33

that was dhosen by people who disdain to say ain't is aren't.

The structure Which describes the two types of negation at this

level is shown in figure 201 where Y indicates the node corresponding

4ocIAS

mk+/19

cleft

11)3

not

Styhed

4r 02.4or, nt

rtoKc e

cmos

3-0

ct.gml(

rer:i

prtference io

pm I hot

Figure 20. Structure of negation

to the node labelled Y in figure 11. Y, it will be recalled, leads to

all the features which require the realization of the empty do if modals,

have, or be are not present. Another feature which has this property

is 221arity emphasis. This also is trivially added to our grammar.

Another feature is a juncture that results after the subject if it is

needed to account for the difference in the number of syllables in 21a

r

34

versus 21b. This example was pointed out by Palmer (1965:33). It is

21a. Now I have gone. [aiv]

21b. Should I have gone [ai av)

Figure 20

an example of a place where syntax affects phonology. This is no

particular problem for the relational network approach. When we need

a syntax connected feature in phonology, we send a signal down to the

phonology from the appropriate place in syntax. There seems to be some

confusion on this point. Postal (1968:118) states: "The stratifica -

tional rejection of phonological or morphophonemic rules which refer

to Surface constituents is..among the clearest evidence of the extent

to which this theory fails to be descriptive of human language." We

do not carry into the phonology all of the information about the

'surface structure ' because we don't need all of it. But, of course,

we bring down any information that is needed. Where these lines enter

the phonology, we call them phonological features, because in general

they come from more than one place in the syntax, or go to more than one

place in phonology, or both. That is, they go through an alternation

pattern. For example, the juncture needed to account for the sentences

in figure 21 also occurs after noun phrases which are not simple pronouns,

as evidenced by the minimal pair in figure 22 where Shei is a nickname

for Sheila (Palmer, 1965:33).

35

22a. Shei'll be there. ( i: al]

22b. She'll be there. ( i: 1]

Figure 22

Postal seems to be objecting both to calling such features phonolo-

gical and to the fact that we bring down only the necessary features,

rather than all features. He feels our approach is ad hoc. However,

Chomsky (1967:108) has pointed out that evaluative notions such as

simplicity are theory specific - the same argument applies to notions

of ad hoc. From the point of view of stratificational grammar, to send

all syntactic information to the phonology when only a few junctures

are needed is like killing a mosquito by dropping an H-bomb on ft. Of

coursed in order to complete the argument, it is necessary to demon-

strate that the transformational cycle is unnecessary to account for

stress in English. This would be a paper in itself (at least), but a

gketch of the argument is given in Reich, forthcoming, and so it will

not be pursued further here.

Figure 23 gives our final tentative sketch of the grammar for

the English auxiliaries, with negation, polarity emphasis, and the

above-mentioned juncture.

The grammar described by figure 23 attached to figure 16 differs

from Newell's (1966) stratificational treatment in two ways. The first

is that it does not follow the 1566 stratificational format. This

has resulted in reducing a certain amount of redundancy that existed

in the earlier treatment. The second difference is that Newell's

treatment causes problems in defining a performance model to fit his

36

IMO

-

Figure 23: Tentative grammar for the

auxiliaries

37

formulation. The morphemic system needs to 'look ahead' to see what

is going to come down from the lexemic stratum before it actually

comes down, in order to handle the insertion of the grammatically deter-

mined do properly. This can be avoided by adding some additional

structure to the morphotactics but it increases bistratal redundancy,

as this additional structure is already in the lexotactics. In order

to demonstrate that my formulation does not suffer from such performance

problems) which can be very difficult to spot, I have tested it on the

computer, using the Relational Network Simulator (Reich, 1968).

Sample output of a slightly earlier version appears in the appendix to

that paper. The definition of the nodes used in running this network

is also given in the appendix. The network produced as required in all

samples tested.

In this paper we have shown that the relational network approach

is adequate to handle the relationship between interrogative and declar-

ative word order, the grammatically determined do, not, and the order

of morphemes in the verbal auxiliary. This is one step toward demon-

strating that the relational netuvrk approach is a viable alternative

way of formalizing our knowledge of English grammar.

Footnotes

38

1In his recent work, Lamb sometimes uses diamonds where I am going

to use upward unordered ands (upward conjunction). This is based on

two considerations. One is that if upward unordered ands are used as

I use them in this paper, they cannot be defined in the same way as

downward unordered ands. I prefer hot to be bound by a constraint

requiring that upward and downward nodes with identical logical function

need necessarily be defined identically. The other consideration is

that he is trying to solve the problem of both language production (en-

coding) and language perception (decoding). In some versions of decoding

it appears that these nodes behave differently with respect to their

two upward wires. If this is the case, then the node cannot be commu-

tative and should be represented differently. I have limited myself

in these papers to the problem of encoding, and in this domain I have

found no reason-to depart from Lamb's (19661) earlier notation.

2Both optional nodes are indicated with a circle on the optional

line. A downward optional is put near the node above it on the line,

and an upward optional is put near the node below it on the line. In

situations where this does not make the difference clear, I indicate

the upward optional by adding a line immediately below the circle, as

shown in figure 2, and the downward optional by adding a line immed-

iately above the circle, as dhown in figure 1.

31 have chosen this model merely for purposes of explicitness.

A two tense description such as that described by Huddleston, Hudson,

Winter and Henrici (1968) has much to recommend it, although I

personally don't agree with all their examples (this is probably a

39

dialect difference). David Bennett and Geoffrey Sampson, working at

Yale, have both found additional evidence for a two tense system.

Since most of the difference would appear in the networks which would

describe English semology, and since this paper is concerned exclu-

sively with lexemic and morphemic structure, itis not important to

the arguments in this paper how the issue is ultimately resolved.

411his is the point in the grammar which would have to be modified

if the semology is better described in terms of a two tense system.

Spe footnote 3.

5This design assumes the signal for negation is one of the first

signals sent down by the semology. Otherwise such non-English strings

as *I will haven't Eat instead of / won't have gone might be produced.

6This is one place in which extensive changes have taken place in

transformational theory since 1957. In my opinion these changes have

only made matters worse, at least with respect to morphophonemic

structure. I have never seen in print how transformationalists propose

to handle this structure within their current flormulation, although

Wall (personal communication) has indicated how he thinks it might be

done. In this paper I will refer only to the 1957 version of transfor-

mational grammar, and save discussion of the newer formulation and the

reason I dislike it, for a future paper.

7The irregularity of have can be handled completely in the phono-

logy by spelling it haV where V is a consonant which is realized as v

only in syllable final position. Thus MN/haVd/ is realized as 13/h ae di/

MNand /haVZ/ is realized as P/hm z/.

40

8After this paper was written Lamb modified his position so that

it might be relatively close to mine. However, it is too early to tell

exactly what the correspondence will be.

9For more discussion on this issue see Lamb, 1564:111ff, Chomsky,

1562c:97, and Lamb's description of the same data in Lamb, 1566b:39.

100ne must not confuse this example with 'Zellig didn't stay at the

hotel; 'he moved into a 'flat., which is grammatical in an appropriate

context.

11Except in the case of the cophiative be, where it occurs after

the main verb.

141

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